where \(w_{k} = 2\alpha c_{k}\)  and \(b_{k} = -\alpha \Vert c_{k} \Vert ^{2}\) . However, in [1]} the authors propose decoupling dependencies of parameters \(c_{k}\) , \(w_{k}\) , and \(b_{k}\)  as it will brings greater flexibility to the model. In this manner NetVLAD layer consists of three independent set of learnable parameters. We crop the ResNet-20 at the last convolutional layer and view it as a \(D\) -dimensional (here \(D = 64\) ) local image descriptor. As depicted in Figure REF  the NetVLAD layer can be decomposed into CNN layers connected in an acyclic graph. Equation (REF ) represents the soft-max activation function. So the soft-assignments of local image descriptor \(x_{i}\)  to clusters \(c_{k}\)  can be viewed as applying a \(1 \times 1\)  convolution layer with \(K\)  filters representing \(w_{k}\)  and biases as \(b_{k}\)  followed by the soft-max activation function to obtain final soft-assignments \({\alpha }_{k}(x_{i})\) . The final output is \(K \times D \times 1\) -dimensional representing the full embedding for local image descriptor \(x_{i}\) .
